To be honest, it surprises me a lot to say this, but of all the airline websites in the world, Qantas is one of the best. It has a lot of information there (and most of it is correct), its booking engine is fairly good and robust, it loads surprisingly quickly and yet still looks OK when rendered on most browsers. (I'm using the latest Firefox on Windows 7 with AdBlockPlus).
The "Flights to" page is probably a bit slow off the mark, so that could use a bit of work (or offer a lo-fi alternative page).
VA's website, for some reason, is slow to respond at times, especially when you accidentally focus on the "mega menus" or expanding sections of the site. In fact, I really don't like the mega menus concept.
The reset problem on QF's website has been a pain for a while. In addition, it'd be nice that when you book an award and select an award type (e.g. Classic or Any Seat), then click "Multi-City", it actually tells you at the top what kind of multi-city you are booking (i.e. Classic multi-city or Any Seat multi-city). At the moment, it doesn't tell you which. It's not a big deal in a sense, but it does help with UI.
I also would've like to have seen the QF FF page change dynamically (viz. skinned or coloured) for status, even if it's just a header or a box (the whole page repainted might not be a good idea), or even a mini-pic of the membership card representing the status attained.
And the new lounge locations page is nice in principle, but readability can be wanting at times, and I really don't like how QF just used random lounge pictures to stand in for the backgrounds when you are viewing different lounge locations each time (it makes no sense to view the information on the ASP lounge and have a picture of a woman enjoying a coffee in the F lounge in the background).